Consider the following strawman scenario: Roommate A is earning a million dollars a year, and the other three are student artists, surviving on odd jobs. Would it be "fair" for roommate A to to pay no more than $215 - $135 = $80/month more than the others, when their ability to pay is so much greater?
That's obviously a contrived example, but not too different from my own situation. I'm a consultant / business owner whose income is not extravagant, but is reasonably above the UK mean. I have a flatmate -- who is fact a student artist -- who contributes roughly 20% of the total costs to the household, including utility & council taxes and whatnot. An 80/20 split may sound terribly inequitable, but we're both paying a similar percentage of our earnings for rent, so it's quite equitable from that perspective.
Absent this arrangement, I could still afford to live on my own, but I'd be left with less cash at the end of the month, and my place would seem a bit empty. My flatmate, in turn, could probably only afford to live in some tiny squalid place far from the city centre. If we were to insist on a 50/50 split which is "fair" from the perspective of the space & utilities (rather than from the perspective our respective pocketbooks), then no accommodation could be found: my flatmate could never afford to pay half the rent. But by optimising around a subjectively fair allocation of our personal resources and preferences, I get an excellent flatmate and more spending money, and they get a much nicer place in London than they could otherwise afford. This is a far better outcome for both of us than we could achieve by insisting on an "objectively fair" split.
As for your chores dilemma: just have a basic rule about not leaving one's personal crap in the common areas. Then for the routine tasks (vacuuming, mopping, etc.), collect an extra $5/week from everybody, and use that money to hire a professional cleaner (or if one of the flatmates is short of cash and particularly good at / enthusiastic about cleaning, pay them to do it). Seriously, it's worth it. People have vastly different capabilities and preferences when it comes to cleaning, and trying to make everybody equal in this respect is an un-winnable game. Don't even try.
tl;dr: the less you strive for egalitarianism through uniformity, and the more you accommodate the divergent abilities and subjective viewpoints of your flatmates, the better you'll be able to find win/win scenarios in shared-living situations.